Bernhard Nebel. A knowledge-level analysis of belief revision. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 301--311, San Francisco, CA, 1989. Morgan Kaufmann. Held Toronto, Canada.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... principles for modelpreference logics [Brown and Shoham, 1989] including for logic programming with negation as failure [Przymusinski, 1988] and terminological logics [Quantz and Royer, 1992] possibilistic logic [Dubois and Prade, 1988] syntax based belief revision formalisms, e.g. [Nebel, 1989] ; and a variety of others, e.g. Brewka, 1989a] Brewka, 1989b] Brewka, 1994] Ginsberg, 1988] Zadrozny, 1987] Pollock, 1987] Konolige, 1988] Ryan, 1992b] Ryan, 1992a] Hunter, 1994] From a practical viewpoint, two very important kinds of non monotonic reasoning, in use even before the ....

Bernhard Nebel. A knowledge-level analysis of belief revision. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 301--311, San Francisco, CA, 1989. Morgan Kaufmann. Held Toronto, Canada.

....general framework for belief change, it is generally accepted that belief sets do not have a rich enough structure to serve as appropriate models for epis temic states [4] One of the proposals to rectify this is to replace belief sets with arbitrary sets of sentences, known as bases. In one view [16], a base should be thought of as providing more structure to its associated belief set, which means that it can be used to determine the belief contraction opera tion associated with a base contraction operation (where the belief contraction operation associat ed with a base contraction ....

Bernhard Nebel. A knowledge level analysis of belief revision. In Ronald J. Brachman, Hec- tor J. Levesque, and Raymond Reiter, editors, Proceedings of the First International Confer- ence on Principles of Knowledge Representa- tion and Reasoning, pages 301-311, San Ma- teo, CA, 1989. Morgan Kaufmann.

....to which the body of knowledge should change as little as possible if new information is incorporated. A well known knowledge change approach is the Set Of Theories approach, a formula based change method first defined in [16] in the context of databases and considered for AI applications e.g. in [22, 38]. This method works as follows. Assume that the sentence p must be incorporated into the knowledge base T , which is a finite set of sentences. If T is consistent with p, then p is simply added to T ; otherwise, is provable from T . In this case, a set R of sentences is removed from T such ....

B. Nebel. A knowledge level analysis of belief revision. In Proc. 1st Intl. Conf. on Principles of Knowledge Representation and Reasoning (KR-89), pp. 301--311, 1989.

....union i=1 K i of the bases, such operators usually do not take into account the frequency Indeed, as in belief revision, giving some importance to the syntax of K i is a way to specify (implicitly but in a cheap way w.r.t. representation) that explicit beliefs are preferred to implicit beliefs [Nebel, 1989; Hansson, 1998] of each explicit pieces of belief into the merging process (the fact that i;j is believed in one source only or in the m sources under consideration is not considered relevant, which is often counter intuitive ) In this paper, a new framework for de ning propositional ....

B. Nebel. A knowledge level analysis of belief revision. In Proc. of KR'89, pages 301-311, 1989.

.... de croyances proposi En fait, tout comme pour la r evision de croyances, donner de l importance a la syntaxe des K i est une mani ere de sp ecifier (implicitement, mais de facon economique vue la repr esentation) que les croyances explicites sont plus importantes que les croyances d eriv ees [20, 8]. Dans [10] l utilisation de fonctions de s election est propos ee pour r esoudre ce probl eme. tionnelles. Nous d efinissons une famille d op erateurs param etr es par une (pseudo )distance d entre interpr etations et par deux fonctions d agr egation f et g. Ces param etres sont utilis es ....

B. Nebel. A knowledge level analysis of belief revision. In Proc. of KR'89, pages 301--311, 1989.

....to Levi identity, the revision functions are obtained by adding the new data to the output of the contraction functions. The main idea is that of simple base contraction, using B#a. Contraction is defined as the intersection of all subsets in B#a. We modify the original notion given in [3] 9] [14] in order to retain the finiteness of the base) A di#erent approach was introduced in [1] for belief sets, but may be easily adapted to belief bases. The safe contraction is the base obtained deleting all possible minimal subsets implying a. Deleting the elements of an incision on B#a transforms ....

Nebel, B., A Knowledge Level Analysis of Belief Revision. In Brachman, R.J., Levesque, H.J., Reiter, R. (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the 1st Int. Conference, pp.301-311,(1989)

....to Levi identity, the revision functions are obtained by adding the new data to the output of the contraction function. The main idea is that of simple base contraction, using B#a. Contraction is defined as the intersection of all subsets in B#a. We modify the original notion given in [3] 9] [14] in order to retain the finiteness of the base) A different approach was introduced by [1] for belief sets, but may be easily adapted to belief bases. The safe contraction is the base obtained deleting all possible minimal subsets implying a. Last, deleting the elements of an incision on B#a ....

Nebel, B., A Knowledge Level Analysis of Belief Revision. In Brachman, R.J., Levesque, H.J., Reiter, R. (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the 1st Int. Conference, pp.301-311,(1989)

....between a basic set of beliefs and their consequences as a small step toward capturing the justificatory structure of an agent s beliefs [4] I shall take a base for a theory T to be a set of formulas B, which may or may not be deductively closed, such that B T. For more on belief bases, see [9, 10] and the references therein) To define Pareto minimal revision of belief bases, I begin again with two ways of making a change to a belief base. If B, B are two bases, I say that B retracts the formula p from B iffp B and p B , and that B adds the formula p to Biff p B and p B . The definition ....

Nebel, B.: 1989, 'A Knowledge Level Analysis of Belief Revision', in: R. J. Brach- man, H. J. Levesque, and R. Reiter (eds.), Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (KR'89), Toronto, Canada, pp. 301-311, Morgan Kaufmann.

....the algorithms of iterated belief revision ( 9] It is also pointed out in [10] where the difference between belief sets (knowledge only) and epistemic states (knowledge including information on how to revise it) is discussed. To achieve the above goals, our method will use Nebel s proposition ([4]) for the selection of the belief base. Nebel proposes the use of a belief base consisting of propositional sentences representing specific observations, experiments, rules etc out of which our knowledge is derived. This approach follows the foundational paradigm, as the propositions in the base ....

....transformation. This model extension can be found in [11] Moreover, the search for the general conditions (parameters) under which the algorithm satisfies the AGM postulates is an ongoing effort, as well as the simulation of other algorithms, like those proposed in [6] and [7] by Williams, in [4] by Nebel etc. ....

Bernhard Nebel, "A Knowledge Level Analysis of Belief Revision", In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pp. 301-311, 1989.

....research. The flrst employs so called belief bases, the second update approach essentially abandons the idea that contraction functions should avoid retractions above all additions, and the third project is the standard AGM axiomatization. Belief Bases. A belief base is just a set of formulas (Nebel 1989; Nebel 1994) Schulte 1999) Hence a belief base is not necessarily closed under logical consequence. What does a belief base represent An interesting interpretation of belief bases is that they capture the fundamental or basic beliefs of an agent. A rational agent will also have other beliefs, ....

....the necessary and su cient conditions for Pareto minimal base revisions. And unlike in the case of theories, consistent retraction minimal contractions do not lead to a deflnite belief about every possible assertion. A sample of papers on base revision with further references is (Nebel 1994) (Nebel 1989), Hansson 1993) Hansson 1998) Meyer 1999) Update:Abandoning Retraction Minimality. Let us return to modelling the agent s beliefs by logically closed theories. In that case the aim of minimizing retractions causes the di culty that it leads to complete beliefs, at least when formulated as ....

Nebel, B. (1989). A knowledge level analysis of belief revision. In Proceedings of the First International Conference on Principles of 42 Oliver Schulte Knowledge Representation and Reasoning, Los Altos, pp. 301-311. Morgan Kaufmann.

....1993 ] Some reasons for this diculty will become clearer later in the paper. A major alternative solution to the problem of belief revision is based on the assumption that our corpus of beliefs is usually generated by some set of basic propositions (see, e.g. Fuhrmann, 1991; Hansson, 1992; Nebel, 1989 ] This base generation approach embodies an important structural aspect of our beliefs that does not nd its proper place in the AGM theory, ii A. BOCHMAN namely that some our beliefs are purely derivative and arise simply as logical consequences of other beliefs we have. It would be natural ....

.... Notice that the majority of current approaches in the base generation camp eventually impose some kind of preference structure on the subsets of the base, which gives an epistemic state of the form (B ; where is some preference relation on B see, e.g. Fuhrmann, 1991; Hansson, 1993b; Nebel, 1989 ] Moreover, in most cases this preference relation is also assumed to satisfy the monotonicity property, mentioned above, though it is restricted now to the theories from B . An important special case is obtained when no preferences are imposed on the elements or subsets of the base. In this ....

B. Nebel. A knowledge level analysis of belief revision. In R. J. Brachman et al., editors, Proc. First Int. Conference on Principles of Knowledge Representation and Reasoning, pages 301-311. Morgan Kauman, 1989.

....an instantiation of a coherentist approach to belief acceptance (see [10] according to which justi cations, or reasons, of our beliefs should not be taken into account in performing belief change. An alternative, more foundational, approach has been suggested by a number of authors (see, e.g. [7, 13, 20]) According to the latter, the corpus of beliefs is seen as generated by some (usually nite) set of propositions called its base. Changes of such 1 base generated belief sets are determined by changes in their underlying bases. Among other virtues, this approach has de nite computational ....

....we were simply wrong in deleting A, and want to restore now our previous belief state. In this case it would be helpful if the original state were remembered in some form in the contracted epistemic state in order to permit its recovery. Actually, a quite similar idea was already used by Nebel [20] in the framework of base change: in order to obtain recovery for a contraction of A from K, the contracted belief set K A should be extended to include A K, where the latter will denote the set of implications A B, for all B 2 K. The added set of implications assigns the contraction a feature ....

B. Nebel, A knowledge level analysis of belief revision, Proc. First Int. Conference on Principles of Knowledge Representation and Reasoning (R. J. Brachman et al., eds.), Morgan Kauman, 1989, pp. 301-311.

....is relational, that is, based on a certain preference relation among the maximal subtheories of the belief set. A major alternative solution to the problem of belief revision is based on an assumption that our corpus of beliefs is usually generated by some set of basic propositions (see, e.g. [4, 9, 17]) This approach embodies an important structural aspect of our beliefs that does not nd its proper place in the AGM theory, namely that some our beliefs serve as reasons, or justi cation, for other beliefs. Accordingly, changes in belief sets are determined on this approach by changes in their ....

B. Nebel, A knowledge level analysis of belief revision, Proc. First Int. Conference on Principles of Knowledge Representation and Reasoning (R. J. Brachman et al., eds.), Morgan Kauman, 1989, pp. 301-311.

....KRR systems and theories in terms of these new concepts and guidelines. Introduction Implemented knowledge representation and reasoning, KRR, systems run into danger when they attempt to implement traditional belief change theories intended for ideal reasoning agents [Alchourr on et al. 1985; Nebel, 1989; Hansson, 1993; 1999] Resource limitations can cause a system that guarantees consistency to fail. This is especially true with commonsense reasoning which requires a large knowledge base and a complex reasoning system. Due to this size and complexity, implemented commonsense systems cannot ....

....thus making them implementable. These altered theories can be used for evaluating and comparing implemented systems. The next section describes the motivations and assumptions, notation and a brief description of why our DOBS formalism should not be confused with a belief base [Hansson, 1999; Nebel, 1989] Sections 2 and 3 give background information about belief revision and some traditional belief revision guidelines and postulates. Sections 4 and 5 discuss our DOBS formalism and terminology and the DOBS postulates and belief revision guidelines. Section 6 discusses and compares several KRR ....

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Bernhard Nebel. A knowledge level analysis of belief revision. In R. J. Brachman, H. J. Levesque, and R. Reiter, editors, Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (KR'89), pages 301--311, 1989.

....INTRODUCTION Consider a knowledge base represented by a theory of some logic, say propositional logic. We want to incorporate into a new fact, represented by a sentence of the same language. What should the resulting theory be A growing body of work (Dalal 1988, Katsuno and Mendelzon 1989, Nebel 1989, Rao and Foo 1989) takes as a departure point the rationality postulates proposed by Alchourr on, Gardenfors and Makinson (1985) These are rules that every adequate revision operator should be expected to satisfy. For example: the new fact must be a consequence of the revised knowledge base. ....

Nebel, B. (1989): "A knowledge level analysis of belief revision", Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, 301--311.

....modifications to S in order to maintain consistency. If holds in the resulting belief state then the counterfactual is true. Competing approaches under this paradigm include those in which beliefs are represented as models [3, 17, 44] and those in which beliefs are represented by formulas [8, 32, 21]. An advantage of the former is insensitivity to the syntax of beliefs whereas the latter, because of its sensitivity to syntax, can support reason maintenance [32] The technical problems surrounding each approach involve which beliefs to discard or add to S in order to maintain consistency with ....

.... include those in which beliefs are represented as models [3, 17, 44] and those in which beliefs are represented by formulas [8, 32, 21] An advantage of the former is insensitivity to the syntax of beliefs whereas the latter, because of its sensitivity to syntax, can support reason maintenance [32]. The technical problems surrounding each approach involve which beliefs to discard or add to S in order to maintain consistency with the counterfactual supposition. These choices are usually determined by some set of preferences or orderings on beliefs. For the most part, preferences have been ....

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Bernhard Nebel. A knowledge level analysis of belief revision. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 301--311, 1989.

....of the form (the numbers refer to locations on the board) If I had taken four when I took five, what would you have done . Could you have won . The focus of Isard s work was primarily on issues of tense, aspect, and modality; in this paper the focus is more on representational issues. Nebel [ 1989; 1992 ] generalized Ginsberg s idea showing that revision on belief bases could be viewed as a special case of revision on belief sets. Belief bases are represented as finite sets of beliefs whereas belief sets are represented as closed sets of beliefs. The work in model based belief revision ....

....OE oe g then A j= but if A is revised with :OE, will no longer hold. In contrast, revision operations based on belief sets usually perform the minimal change with respect to some minimality criteria to models of A consistent with OE and so would hold in the revised belief set. As Nebel [ 1989 ] has shown, however, revision operations on belief bases can be viewed as equivalent to revisions on belief sets in which a certain subset of the belief set is taken as foundational; other beliefs will be assumed to be derived. As we shall see, this is accomplished by imposing an ordering on ....

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Nebel, Bernhard 1989. A knowledge level analysis of belief revision. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning. 301--311.

.... will be used to describe a belief space or belief set that has no known contradictions (unless otherwise noted) Even research on finite belief bases still refers to deductive closure in its determination of consistency or when considering belief revision postulates (Hansson 1993a; 1993b; Nebel 1989; Alchourr on Makinson 1985) Consistency is determined by the presence of a contradiction in the implicit beliefs of a belief base. How can this reliably be implemented Even if it can be simulated on a small scale knowledge base, the theories developed might be suspect if applied to a very ....

....determined by the presence of a contradiction in the implicit beliefs of a belief base. How can this reliably be implemented Even if it can be simulated on a small scale knowledge base, the theories developed might be suspect if applied to a very large system. Nebel voiced these concerns as well (Nebel 1989). We address the need to formalize theories that take into account the fact that deductive closure cannot be guaranteed in a real world, need based, implemented system even if the system is restricted by something as simple as the user needing a response within one minute. These theories need ....

Nebel, B. 1989. A knowledge level analysis of belief revision. In Brachman, R. J.; Levesque, H. J.; and Reiter, R., eds., Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (KR'89), 301--311.

....in the same epistemic state and therefore, if faced with the same information, will revise its beliefs in the same way. Recent work on belief revision and update has shown this assumption has very powerful consequences, not always welcome [6, 1, 2] Earlier work on belief base revision (see e.g. [8]) expresses a similar concern about the fundamentals of belief revision. We do not wish to take a stand on the question of whether this identi cation of epistemic states with belief sets is reasonable for the study of belief revision, but we want to point out that, in the study of belief update, ....

B.Nebel. A Knowledge Level Analysis of Belief Revision. In Proceed. First International Conference on Principles of Knowledge Representation and Reasoning, Toronto, 1989.

....of a belief set due to its logical closure definition, and the epistemic entrenchment ordering of beliefs after a belief revision operation cannot be determined by the theory. These issues have been taken up by researchers such as proposals for entrenchment on finite bases of belief revision [Nebel, 1989; Doyle, 1991; Williams, 1992; Nayak, 1994] Other related studies on dynamic belief changes include belief updates [Katsuno and Medelzon, 1989] and expectation theory [G ardenfors, 1991; Gardenfors and Makinson, 1994] 1.1.5 Neural Logic Network Neural networks have been studied mainly for ....

Bernhard Nebel. A knowledge level analysis of belief revision. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (KR'89), pages 301--311, Toronto, Canada, 1989. Morgan Kaufmann.

.... the revision operator rev op by rev op(w) f (revisions (w) Is this rational In lack of a standard for rationality including defaults we can merely state that in the limiting case when the set of defaults is empty, the revision operator rev op behaves like a base contraction operator (as in [Nebel 89] Fuhrmann 91] When lifted to the theory level, it satisfies the basic Grdenfors postulates (except the questionable recovery postulate [Makinson 87] 4.2.1 Exploiting Logical Relations The operator is surprisingly powerful in diagnostic contexts. By definition it avoids target worlds where ....

....Therefore, Nejdl in essence compares different diagnoses while we compare different worlds and thereby sets of diagnoses. The problem of guiding the diagnostic process is an instance of the more general belief revision problem. This is an active research area within AI, e.g. Doyle 91] Nebel 89, 91] that should have a major impact on diagnosis in the future.The notions developed so far, however, e.g. epistemic entrenchment [Grdenfors 88] are important, but not strong enough to provide guidelines for diagnostic processes. 8. Conclusion We have presented a framework for organizing ....

B. Nebel, A Knowledge Level analysis of Belief Revision, Proc. KR '89, Morgan Kaufmann, 1989

....12 on the extensional part of the KB. Both of these updates satisfy the integrity constraints. However, only the first update satisfies the integrity constraints if we are given the further update insert mother(Joan; Bob) The general problem of belief revision has been studied formally in [42, 91, 92, 21]. Gardenfors proposes a set of axioms for rational belief revision containing such constraints on the new theory as no change should occur to the theory when trying to delete a fact that is not already present and the result of revision should not depend on the syntactic form of the new data . ....

....be integrated with improvements of the abductive 63 proof procedure considered in isolation. We have seen that the process of belief revision also needs to be considered within a KA context. In particular, it could be useful to investigate relationships between the belief revision frameworks of [21, 42, 91, 92] and various integrity constraint checking and restoration procedures. The extension of logic programming to include integrity constraints is useful both for abductive logic programming and for deductive databases applications. We have seen, however, that for many applications the use of ....

Nebel, B., A knowledge level analysis of belief revision. Proc. 1st International Conference on Principles of Knowledge Representation and Reasoning, Toronto (1989) 301--311

....Minimality of Change which states that the knowledge base should change as little as possible if new information is incorporated. In this paper we deal with the following methods of updating knowledge bases: Ginsberg s approach [19] also considered by Fagin, Ullman, and Vardi [13] and by Nebel [44, 45], An extended abstract of this paper appeared in the proceedings of the Eleventh ACM SIGACTSIGMOD SIGART Symposium on Principles of Database Systems, San Diego, CA, June 2 4, 1992. y Mailing address: Paniglgasse 16, A 1040 Wien, Austria. Internet e mail: ....

....with new knowledge p, a straightforward method to gain consistency with p is to remove formulas from the knowledge base. This approach apparently injures the principle of Irrelevance of Syntax in knowledge base change, and is thus rejected by many researchers; but it also has its defenders, cf. [19, 44], and there are scenarios which illustrate the need to differentiate in some epistemic contexts between syntactically deviating descriptions of the world [31] Nebel points out an important relation between formula based and model based change, however, showing that formulabased change operators ....

[Article contains additional citation context not shown here]

B. Nebel. A Knowledge Level Analysis of Belief Revision. In Proceedings KR-89, pages 301--311, 1989.

....P 2 P red is a k ary predicate, x 1 ; x n are terms, and t 2 TC [ TV , then [t; P (x 1 ; x n ) is a wff (read as: P (x 1 ; x n ) is true at time t) 5 The new information may be inconsistent with the agent s current beliefs. We leave this for future discussion. See for example, [6,26,53,96,166,103,125,22,66,27]. 6 Our intention model is closer to Shoham [138] s Dec and Thomas et al. 152] s Comit than to Cohen s and Levesque [16] s Intend . 7 We have extended [152] to deal with the FOL case. We prefer this approach, where time can be expressed explicitly, over others where time periods cannot be ....

B. Nebel. A knowledge level analysis of belief revision. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 301--311. Morgan Kaufmann, May 1989.

....Bob) on the extensional part of the KB. Both of these updates satisfy the integrity constraints. However, only the rst update satis es the integrity constraints if we are given the further update insert mother(Joan; Bob) The general problem of belief revision has been studied formally in [42, 91, 92, 21]. G ardenfors proposes a set of axioms for rational belief revision containing such constraints on the new theory as no change should occur to the theory when trying to delete a fact that is not already present and the result of revision should not depend on the syntactic form of the new data . ....

....to be integrated with improvements of the abductive proof procedure considered in isolation. We have seen that the process of belief revision also needs to be considered within a KA context. In particular, it could be useful to investigate relationships between the belief revision frameworks of [21, 42, 91, 92] and various integrity constraint checking and restoration procedures. The extension of logic programming to include integrity constraints is useful both for abductive logic programming and for deductive databases applications. We have seen, however, that for many applications the use of ....

Nebel, B., A knowledge level analysis of belief revision. Proc. 1st International Conference on Principles of Knowledge Representation and Reasoning, Toronto (1989) 301-311

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